Upvote:1
If, as you said, the visa is multiple entry, then you certainly can travel multiple times to any of the Schengen countries, regardless where you are travelling from. Note that UK is not part of the Schengen area and therefore when you go back to UK, you are leaving Schengen area.
As with any Schengen visas though, your first trip should be to the country that issued the visa - either entering it directly or entering via another country with the intention of spending most of the trip in that country. After that, you can go to any other Schengen country without any restrictions - as long as the visa remains valid.
Further note that first trip being to the country that issued the visa is not really mandatory, but if you don't visit the issuing country, it may become a problem if you then apply for another visa later.